What is the integral from 0 to 2 of x^4ln(2x) ?

The integral from 0 to 2 of x^4ln(2x) is 64/5 ln(2)-32/25

Popular >

integral from 0 to 2 of x^4ln(2x)

\int_{0}^{2} x^{4} ln (2 x) d x

\frac{64}{5} ln (2) - \frac{32}{25}

Solution steps

\int_{0}^{2} x^{4} ln (2 x) d x

Apply Integration By Parts

: [\frac{1}{5} x^{5} ln (2 x) - \int \frac{x ^{4}}{5} d x]_{0}^{2}

= [\frac{1}{5} x^{5} ln (2 x) - \int \frac{x ^{4}}{5} d x]_{0}^{2}

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= [\frac{1}{5} x^{5} ln (2 x) - \frac{x ^{5}}{25}]_{0}^{2}

Compute the boundaries:

\frac{64}{5} ln (2) - \frac{32}{25}

= \frac{64}{5} ln (2) - \frac{32}{25}

\int_{0}^{2} 2 π x 1 + 4 x^{2} d x

\int_{0}^{l n (x)} e^{- y} d y

\int_{0}^{\frac{x}{4}} tan^{3} (x) d x

\int_{0}^{9} x e^{- \frac{x}{3}} d x

\int_{- 1}^{0} x^{3} - 6 x d x

What is the integral from 0 to 2 of x^4ln(2x) ?
The integral from 0 to 2 of x^4ln(2x) is 64/5 ln(2)-32/25